Is it permissible for a woman who has undergone major surgery and fears she will not be able to fast due to her inability to eat but very little, to abstain from fasting Ramadan entirely, and what is the expiation for her not fasting in this case?

If your mother is forced to reduce her food intake to avoid vomiting: 1. If the doctor determines that fasting will harm her: She should break her fast and make up the days she missed. 2. If it is merely weakness or fatigue: It is not permissible for her to break her fast. She must intend to fast from the night before and eat a suhoor that will not harm her. If she vomits involuntarily, her fast is valid. 3. If fasting results in apparent hardship: She should break her fast only as much as necessary to maintain her strength, then refrain from eating for the rest of the day and make up that day later.

Notes: If she breaks her fast due to a doctor's order or apparent hardship, she is only required to make up the missed days. Feeding the poor (al-it'am) is only for those whose recovery is not expected, or for elderly individuals who are unable to fast. Breaking the fast without a valid excuse is a major sin.